General Non-Local Continuum Mechanics: Derivation of Balance Equations

In this paper, mechanics of continuum with general form nonlocality in space and time is considered. Some basic concepts nonlocal are discussed. General fractional calculus (GFC) vector (GFVC) used as mathematical tools for constructing media time. Balance equations mass, momentum, energy, which describe conservation laws continuum, derived by using the fundamental theorems GFC. The balance equation integral second first GFC proposed analogue Titchmarsh theorem to derive differential from equations. Using calculus, energy also suggested a wide class regions surfaces.